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Binary pulsars as tools to study gravity
 

Binary pulsars as tools to study gravity

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AIMS seminar by Dr Rene Breton, July 2013

AIMS seminar by Dr Rene Breton, July 2013

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    Binary pulsars as tools to study gravity Binary pulsars as tools to study gravity Presentation Transcript

    • René Breton University of Southampton African Institute for Mathematical Sciences Cape Town, 17 July 2013 Binary Pulsars as Tools to Study Gravity © Daniel Cantin / McGill University Friday 02 August 2013
    • By the End You Should Remember... Binary pulsars • Excellent tools to test gravity • Probe a different gravitational field regime • System diversity = complementarity © Daniel Cantin / McGill University Friday 02 August 2013
    • Pulsars 101 Friday 02 August 2013
    • Pulsars 101 What are pulsars? Radio pulsars are… • Highly magnetized rapidly spinning neutron stars: • Radius ~ 10 km • Mass ~ 1.4 Msun • B-field ~ 1012 Gauss • Pspin ~ 1ms - 10 sec • “Lighthouse effect”: radio waves emitted along the magnetic poles. © Michael Kramer JBCA, University of Manchester © Mark A. Garlick Friday 02 August 2013
    • Pulsars 101 What are pulsars? Radio pulsars are… • Highly magnetized rapidly spinning neutron stars: • Radius ~ 10 km • Mass ~ 1.4 Msun • B-field ~ 1012 Gauss • Pspin ~ 1ms - 10 sec • “Lighthouse effect”: radio waves emitted along the magnetic poles. © Michael Kramer JBCA, University of Manchester © Mark A. Garlick Friday 02 August 2013
    • The Pulsar Population The P-P diagram Fundamental parameters: • Spin period • Spin period derivative Credit: Kramer and Stairs (2008)  Friday 02 August 2013
    • The Binary Pulsar Population Binary pulsars are “special” According to the ATNF catalogue: • 2008 pulsars • 186 binary pulsars Credit: Kramer and Stairs (2008) Binaries: • Short spin periods • Old • Low magnetic fields Friday 02 August 2013
    • The Binary Pulsar Population Binary pulsars are “special” According to the ATNF catalogue: • 2008 pulsars • 186 binary pulsars Credit: Kramer and Stairs (2008) Binaries: • Short spin periods • Old • Low magnetic fields Friday 02 August 2013
    • φ = φ0 + ν(t − t0) + 1 2 ˙ν(t − t0)2 + . . . Binary Pulsar Timing and Gravity Almost textbook examples Compact objects (point mass) Precise timing (frequency standard) Typical TOAs precision is ~0.1% Pspin Friday 02 August 2013
    • Binary Pulsar Dynamics & Relativistic Effects Friday 02 August 2013
    • Newtonian orbits Timing binary pulsars allows one to determine 5 Keplerian parameters: • Orbital period • Eccentricity • Longitude of periastron • Projected semimajor axis • Epoch of periastron Arpad Horvath (Wikipedia) We measure radial Doppler shifts only… => The orbital inclination angle is unknown. Binary Pulsar Timing Friday 02 August 2013
    • Post-Keplerian (PK) parameters: dynamics beyond Newton. • PKs are phenomenological corrections (theory-independent). • PKs are functions of Keplerian parameters, M1 and M2. Esposito-Farese (2004) Binary Pulsar Timing Relativistic orbits More than 2 PKs = test of a given relativistic theory of gravity. Friday 02 August 2013
    • • Testing gravity relies on orbital dynamics • Ideally: pulsar + neutron star eccentric + compact orbit • About 12 known “relativistic” pulsar binaries Binary Pulsar Timing Relativistic orbits4 Weisberg & Taylor Figure 1. Orbital decay of PSR B1913+16. The data points indicate the observed change in the epoch of periastron with date while the parabola illustrates the theoretically expected change in epoch for a system emitting gravitational radiation, according to general relativity. PSR B1913+16 • First binary pulsar discovered (Hulse & Taylor 1975) • First indirect evidence of gravitational wave emission (Taylor et al. 1979) Weisberg & Taylor (2005) Friday 02 August 2013
    • The Double Pulsar (PSR J0737-3039A/B), is the only known pulsar-pulsar system. Pulsar A: 23 ms (Burgay et al., 2003) Pulsar B: 2.8 s (Lyne et al., 2004) Eccentricity: 0.08 Orbital period: 2.4 hrs !!! (vorbital ~ 0.001 c) © John Rowe Animation Australia Telescope National Facility, CSIRO The Double Pulsar A unique system Friday 02 August 2013
    • Periastron advance Rate of precession of the periastron: 17°yr-1 ! It takes 21 years to complete a cycle of precession. The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Periastron advance Rate of precession of the periastron: 17°yr-1 ! It takes 21 years to complete a cycle of precession. The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Gravitational redshift and time dilation Needs to climb to potential well Clocks tick at variable rate in gravitational potentials The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Gravitational redshift and time dilation Needs to climb to potential well Clocks tick at variable rate in gravitational potentials The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Orbital period decay Gravitational wave emission Orbit shrinks 7mm/day (coalescence timescale ~ 85 Myrs) The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Orbital period decay Gravitational wave emission Orbit shrinks 7mm/day (coalescence timescale ~ 85 Myrs) The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Orbital period decay Gravitational wave emission Orbit shrinks 7mm/day (coalescence timescale ~ 85 Myrs) Kramer et al., 2006 Double neutron star merger as seen by a theoretician A B BH The Double Pulsar Testing gravity Friday 02 August 2013
    • Shapiro delay Light travels in curved space-time The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Shapiro delay Light travels in curved space-time The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Shapiro delay Light travels in curved spacetime The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Mass ratio Double Pulsar only: mass ratio, R. MA/MB = aBsin(i) / aAsin(i) (theory-independent; at 1PN level at least) The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Mass ratio Double Pulsar only: mass ratio, R. MA/MB = aBsin(i) / aAsin(i) (theory-independent; at 1PN level at least) The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Testing GR and gravity Mass ratio + 5 PK parameters => Yields 6-2=4 gravity tests Best binary pulsar test Shapiro delay “s” parameter Agrees with GR within 0.05% (Kramer et al. 2006) Hulse-Taylor pulsar is 0.2% The Double Pulsar Testing gravity Kramer et al., 2006 Friday 02 August 2013
    • Precession of the spin angular momentum of a body is expected in relativistic systems. Parallel transport in a curve space-time changes the orientation of a vector relative to distant observers. Known as “geodetic precession” or “de Sitter – Fokker precession”. Relativistic Spin Precession Spin-orbit coupling induces relativistic spin precession Friday 02 August 2013
    • Ωobs = 0.44 +0.48(4.6) −0.16(0.24) ◦ /yr Changes of pulse shape and polarization over time. PSR B1913+16 (Kramer 1998, Weisberg & Taylor 2002, Clifton & Weisberg 2008): • Assume the predicted GR rate to map the beam PSR B1534+12 (Stairs et al. 2004): • Relativistic Spin Precession Observational evidence of precession GEOMETRY OF PSR B1913]16 857 FIG. 1.ÈPulse proÐle of B1913]16 observed in 1995 April At Ðrst, we measured the amplitude ratio of the leading and trailing components using the o†-pulse rms as an uncertainty estimator. These are presented in Figure 2, where we also plot data from It is seen that the newWRT. data are in good agreement with the earlier measured trend. Performing a weighted least-squares Ðt, we obtained a ratio change of [1.9% ^ 0.1% per year. It is interesting to note that our Ðt is also in agreement with the component ratio from 1978 March which was measured using the(Fig. 2), proÐle published by & Weisberg The ampli-Taylor (1982). tude ratio between proÐle midpoint and trailing component seems to remain constant at a value of about 0.17 over a time span of 20 yr within the errors. Measuring the separation between the leading and trail- ing components, we followed the approach of byWRT Ðtting Gaussian curves to the central portion of each com- ponent. The formal accuracy determined by the Ðt error can be up to an order of magnitude better than the sampling time, similar to a standard template matching procedure. We note, however, that the components are asymmetric in shape, so that the resulting centroids might be a†ected by FIG. 2.ÈAmplitude ratio of leading and trailing components as a func- tion of time. Filled circles were adapted from while open circlesWRT, represent E†elsberg measurements. The dashed line represents a linear Ðt FIG. 3.È Closed circ surements p listed in Tab the consiste details). the numb In order t tainty, we to intensi respective and their with valu approach 1981 proÐ levels. W agreemen consisten In wha general re the uncer beam exh with inte The Ðrst excellent prediction Wh1989). magnetic change, t ΩGR = 0.51◦ /yr Kramer 1998 Friday 02 August 2013
    • Pulsar A eclipsed by pulsar B for ~30 seconds at conjunction Rapid flux changes synchronized with pulsar B’s rotation (McLaughlin et al. 2004) A B Time of arrival of B’s pulse Double Pulsar Eclipses Phenomenology Breton et al. 2008 Friday 02 August 2013
    • Double Pulsar Eclipses Modeling using synchrotron absorption in a truncated dipole The “doughnut model” (Lyutikov & Thompson 2006) Friday 02 August 2013
    • Double Pulsar Eclipses Modeling using synchrotron absorption in a truncated dipole The “doughnut model” (Lyutikov & Thompson 2006) Friday 02 August 2013
    • Double Pulsar Eclipses Modeling using synchrotron absorption in a truncated dipole Breton et al. 2008 Friday 02 August 2013
    • Double Pulsar Eclipses Modeling using synchrotron absorption in a truncated dipole Breton et al. 2008 Friday 02 August 2013
    • Empirical evidence of dipolar magnetic field geometry. Eclipses are a proxy to infer the orientation of pulsar B. Double Pulsar Eclipses It works! Breton et al. 2008 A B Friday 02 August 2013
    • Quantitative measurement of relativistic spin precession. Testing General Relativity in a Strong Field General relativity passes the test once again! Breton et al. 2008 Friday 02 August 2013
    • Quantitative measurement of relativistic spin precession. Testing General Relativity in a Strong Field General relativity passes the test once again! Breton et al. 2008 Friday 02 August 2013
    • Pulsar B disappeared in 2009... so no more “Double Pulsar” Testing General Relativity in a Strong Field By the way... Friday 02 August 2013
    • Pulsar B disappeared in 2009... so no more “Double Pulsar” Testing General Relativity in a Strong Field By the way... 2024 Friday 02 August 2013
    • Testing Theories of Gravity Friday 02 August 2013
    • “Strong-field” regime: • Still > 250 000 RSchwarzchild in separation but… • Ebinding ~ 15% Etot Esposito-Farese (2004) Strong-field regime Why are tests of gravity involving pulsars interesting? Friday 02 August 2013
    • Generalized precession rate is (Damour & Taylor, 1992, Phys. Rev. D): In terms of a very particular choice of observable timing parameters: Theory-Independent Test of Gravity Unique test... for a unique double pulsar... Friday 02 August 2013
    • Generalized precession rate is (Damour & Taylor, 1992, Phys. Rev. D): In terms of a very particular choice of observable timing parameters: Test of the strong-field parameters . Any other mixture of timing observables would include additional strong-field parameters. Theory-Independent Test of Gravity Unique test... for a unique double pulsar... Friday 02 August 2013
    • Generalized precession rate is (Damour & Taylor, 1992, Phys. Rev. D): In terms of a very particular choice of observable timing parameters: Test of the strong-field parameters . Any other mixture of timing observables would include additional strong-field parameters. The Double Pulsar is the only double neutron star system in which both semi- major axes can be measured independently! Theory-Independent Test of Gravity Unique test... for a unique double pulsar... Friday 02 August 2013
    • Mass ratio from pulsar timing + white dwarf spectroscopy Dipolar Gravitational Waves and MOND The pulsar-white dwarf binary PSR J1738+0333 10 Freire, Wex, Esposito-Far`ese, Verbiest et al. mc Pb . Pb . mc qq Figure 5. Constraints on system masses and orbital inclination from radio and optical measurements of PSR J1738+0333 and its WD companion. The mass ratio q and the companion mass mc are theory-independent (indicated in black), but the constraints from the measured intrinsic orbital decay ( ˙P Int b , in orange) are calculated assuming that GR is the correct theory of gravity. All curves intersect, meaning that GR passes this important test. Left: cos i–mc plane. The gray region is excluded by the condition mp > 0. Right: mp–mc Freire et al. (2012) & Antoniadis et al. (2012) White dwarf mass from photometry + spectroscopy Orbital period decay from pulsar timing Freire et al. (2012) & Antoniadis et al. (2012) Friday 02 August 2013
    • ˙Pxs b = ˙P ˙M b + ˙PT b + ˙PD b + ˙P ˙G b ˙PD b ￿ −2π nbT⊙mc q q + 1 κD(spsr − scomp)2 spsr,comp ￿ ￿/Mpsr,compc2 The “excess” orbital period decay: Dipolar Gravitational Waves and MOND Constraining dipolar gravitational waves mass loss tides dipolar gravitational waves variation of gravitational constant where Friday 02 August 2013
    • ˙Pxs b = ˙P ˙M b + ˙PT b + ˙PD b + ˙P ˙G b ˙PD b ￿ −2π nbT⊙mc q q + 1 κD(spsr − scomp)2 spsr,comp ￿ ￿/Mpsr,compc2 The “excess” orbital period decay: Dipolar Gravitational Waves and MOND Constraining dipolar gravitational waves mass loss tides dipolar gravitational waves variation of gravitational constant spsr ￿= scomp Neutron star + white dwarf binaries have very different self-gravity where Friday 02 August 2013
    • ˙PD b ˙P ˙G b Dipolar Gravitational Waves and MOND Constraining dipolar gravitational waves The most stringe Figure 6. Limits on ˙G/G and κD derived from the measurements of ˙P xs b of PSR J1738+0333 and PSR J0437−4715. The inner blue contour level includes 68.3% and the outer contour level 95.4% seem particu in the comp system make alternative g the emission 5 and 6, we classes of gra more generic perturbative contribution of the bodies does not car ple, the well theory falls i Under t change in th radiation dam ˙PD b −2π n are degenerateand Combining data from PSRs J1738+0333 and J0437-4715 breaks the degeneracy Freire et al. (2012) and, also, Lazaridis et al. (2009) Lunar Laser Ranging Friday 02 August 2013
    • ln A(ϕ) − ln A(ϕ0) = α0(ϕ − ϕ0) + 1 2 β0(ϕ − ϕ0)2 ˜GAB ≡ G∗A2 (ϕ0) · (1 + αAαB) γAB ≡ 1 − 2 αAαB 1 + αAαB βA BC ≡ 1 + 1 2 βAαBαC (1 + αAαB)(1 + αAαC) ˜gµν ≡ A2 (ϕ)gµν Dipolar Gravitational Waves and MOND Constraining tensor-scalar theories Freire et al. (2012) Associated metric A general tensor scalar field Modify the behavior of gravitational constant And the Eddington’s PPN parameters t al. e a- D t s- s r- r × n ) ). r ) t l. t e n- n s a LLR LLR SEP J1141–6545 B1534+12 B1913+16 J0737–3039 J1738+0333 −6 −4 −2 2 4 6 0 0 0 0| 10 10 10 10 10 Cassini Figure 7. Solar-system and binary pulsar 1-σ constraints on the matter-scalar coupling constants α0 and β0. Note that a log- arithmic scale is used for the vertical axis |α0|, i.e., that GR (α0 = β0 = 0) is sent at an infinite distance down this axis. LLR stands for lunar laser ranging, Cassini for the measure- ment of a Shapiro time-delay variation in the Solar System, and GR Friday 02 August 2013
    • βA BC ≡ 1 + 1 2 βAαBαC (1 + αAαB)(1 + αAαC) ˜g00 = A2 (ϕ)g00 ˜gij = A−2 (ϕ)gij ˜GAB = G∗(1 + αAαB) γAB = γPPN = 1 Dipolar Gravitational Waves and MOND Constraining modified newtonian dynamics Freire et al. (2012) Associated metric MOND is the non-relativistic limit of tensor-vector-scalar (TeVeS) theories Modify the behavior of gravitational constant And the Eddington’s PPN parameters GR t al. e a - s n , i 0 s 5 n w r e n σ s - - ) V - h r , t LLR SEP J1141–6545 B1534+12 B1913+16 J0737–3039 J1738+0333 10 −6 −4 −2 0 2 4 6 0 0| 100 Tuned TeVeS Inconsistent TeVeS 10 10 10 Figure 8. Similar theory plane as in Fig. 7, but now for the (non- conformal) matter-scalar coupling described in the text, general- izing the TeVeS model. Above the upper horizontal dashed line, the nonlinear kinetic term of the scalar field may be a natural function; between the two dashed lines, this function needs to be tuned; and below the lower dashed line, it cannot exist any and Friday 02 August 2013
    • Dipolar Gravitational Waves and MOND The pulsar-white dwarf binary PSR J1738+0333 Antoniadis et al. (2013) Antoniadis et al. (2013) MWD MWD P . b P . b qq New system discovered that provides even better constraints. Might rule out MOND within the next few years. Friday 02 August 2013
    • |ˆα3| < 5.5 × 10−20 |∆| < 4.6 × 10−3 P2 orb/e2 P2 orb/(eP) P 1/3 orb /e Pulsar + WD in low eccentricity wide orbit Test strong equivalence principle Test violation of momentum conservation and preferred frame-effects More Tests of Gravity? SEP violation, preferred-frame effects statistical: see, e.g., Gonzalez et al. 2011, Stairs et al. 2005 individual system: see, e.g., Wex & Kramer 2007 Friday 02 August 2013
    • Neutron Star Equation-of-State Probing the upper mass limit of neutron stars PSR B1957+20 PSR J1614-2230 Lattimer 2007 van Kerkwijk, Breton & Kulkarni (2011) Demorest et al. (2010) Friday 02 August 2013
    • The Future Is Bright More pulsars, more photons More pulsars: What if we know “all” pulsars from the Galaxy? More binaries = many new oddballs Not clear how this translates for gravity tests More photons: Accurate parallax for large number of pulsars Improved timing on existing systems Friday 02 August 2013
    • Conclusions Eccentricity OrbitalPeriod PSR + NS PSR + WD spin-orbit coupling dipolar GW tensor-scalar TeVeS/MOND NS EoS SEP preferred-frame effects (individual) preferred-frame effects (statistical) variation of G consistencies of theories relativistic effects Binary pulsars • Excellent tools to test gravity • Probe a different gravitational field regime • System diversity = complementarity PSR + BD* Friday 02 August 2013